Efficient Grid Search to Solve Static Games with Private Information

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We introduce a new method for computing equilibria in a large class of games, including auctions, nonlinear pricing and optimal contracting. First, we observe that the objective function, e.g. the bid function in an auction, can often be approximated arbitrarily well by a piecewise constant function. Second, we formulate a sequential program to find the global solution within this class of strategies. This presents a major advantage over other solution methods which rely on local optimization. A Monte Carlo study of asymmetric auctions and nonlinear pricing games suggests that the method is stable, fast, and easily extends to complex games that are difficult to solve with existing methods. We then examine two applications to highway procurement auctions and show that our method leads to increases in accuracy and speed, and has fewer required model restrictions. Finally, we use our method to shed light on recent concerns of shrinkflation. We study the breakfast cereal market and compute globally incentive-compatible counterfactual package size and price adjustments following a cost shock.